Different latent class models were used and evaluated for assessing the accuracy of campylobacter diagnostic tests: overcoming imperfect reference standards?

Abstract

In the absence of perfect reference standard, classical techniques result in biased diagnostic accuracy and prevalence estimates. By statistically defining the true disease status, latent class models (LCM) constitute a promising alternative. However, LCM is a complex method which relies on parametric assumptions, including usually a conditional independence between tests and might suffer from data sparseness. We carefully applied LCMs to assess new campylobacter infection detection tests for which bacteriological culture is an imperfect reference standard. Five diagnostic tests (culture, polymerase chain reaction and three immunoenzymatic tests) of campylobacter infection were collected in 623 patients from Bordeaux and Lyon Hospitals, France. Their diagnostic accuracy were estimated with standard and extended LCMs with a thorough examination of models goodness-of-fit. The model including a residual dependence specific to the immunoenzymatic tests best complied with LCM assumptions. Asymptotic results of goodness-of-fit statistics were substantially impaired by data sparseness and empirical distributions were preferred. Results confirmed moderate sensitivity of the culture and high performances of immunoenzymatic tests. LCMs can be used to estimate diagnostic tests accuracy in the absence of perfect reference standard. However, their implementation and assessment require specific attention due to data sparseness and limitations of existing software.

Keywords: Campylobacter; diagnostic accuracy; imperfect gold standard; latent class model; sparseness.

Fig. 1.

Diagram (left panel) and corresponding profile probability (right panel) for three latent class models assuming different dependence structures, CampyLCA study, France, 2016. LCM CI, latent class model under conditional independence; LCM CD, latent class model with a residual dependence common to all tests; LCM SD, latent class model with a residual dependence specific to the three immunoenzymatic tests. Ovals and rectangles indicate latent quantities and observed quantities, respectively: D = 0/1: unobserved presence/absence of campylobacter infection; T₁: Culture Karmali; T₂: Real-time PCR; T₃: Ridascreen^®; T₄: Premier^®Campy^®; T₅: ImmunoCardStat!^®Campy; u: random residual dependence which follows a standard Gaussian distribution. In the equations, t_k+ and t_k− indicate a positive and negative result for test T_k, respectively; Φ is the standard cumulative Gaussian distribution function; parameters to estimate are (a_kd)k = 1,…,K, d = 0, 1 for the probit transformations of sensitivities and specificities, μ for the logit transformation of the prevalence and σ for the intensity of the individual random deviation.

Fig. 2.

Evaluation of local independence hypothesis by residual correlations and their 95% confidence interval, as well as by P-values of bivariate statistics, CampyLCA study, France, 2016. (a) Residual correlations for latent class model under conditional independence; (b) Residual correlations for latent class model with a residual dependence common to all tests; (c) Residual correlations for latent class model with a residual dependence specific to the three immunoenzymatic tests. T₁: Culture Karmali; T₂: Real-time PCR; T₃: Ridascreen^®; T₄: Premier^®Campy; T₅: ImmunoCard Stat!^®Campy. Residual correlations presented with dots (point estimates) and bars (95% confidence intervals). P-values of bivariate statistics are provided above each pair of tests described on the horizontal axis.

Fig. 3.

Diagnostic accuracy estimates (point estimate and 95% confidence interval) of campylobacter infection tests according to the LCM SD model and to culture as the reference standard, CampyLCA study, France, 2016. LCM SD, latent class model with a residual dependence specific to the three immunoenzymatic tests; Ref Std: culture Karmali.